A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

Question

DivineJEE · Accepted Answer

(a) : The team can have either 0 boy or 1 boy. So the number of selections is ( ^6 C_4 * ^4 C_0+ ^6 C_3 * ^4 C_1) * ^4 C_1 = (15 + 20 * 4) * 4 = 95 * 4 = 380

Explanation

For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

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